Chickpea protein isolate was hydrolyzed using Flavourzyme immobilized on glyoxyl-agarose beads by multipoint covalent attachment. This Flavourzyme-glyoxyl derivative, produced after 1 h of immobilization at 4 °C followed by 5.5 h at room temperature, presented approximately 51% of the endoprotease activity of Flavourzyme but was around 700 times more stable than soluble enzyme. Chickpea protein hydrolysates ranging from 1% to 10% degree of hydrolysis were produced and their chemical composition was very close to that of protein isolate used as starting material. Solubility, oil absorption, emulsifying activity and stability, and foaming capacity and stability were determined. All protein hydrolysates showed higher solubility than intact proteins, especially at pHs near isoelectric point of native chickpea proteins. Moreover, all hydrolysates had better functional properties, except emulsifying activity, than the original protein isolate.